Task: High Altitude Weather Balloons and the Ideal Gas Law

Phenomenon

When a sealed weather balloon is released from the ground, it expands significantly as it rises high into the atmosphere. The balloon starts out partially inflated but grows very large, sometimes even bursting, as it reaches higher altitudes where the temperature is freezing and the atmospheric pressure is extremely low.

Performance Expectation

Estimated Time: 45-60 minutes Materials: Computer or tablet with internet access, student handout, Ideal Gas Law Derivation (Scaffolded) simulation.

HS-PS3-2: Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).

Part 1: Engage (Anchoring Phenomenon)

Instructions: Imagine a large weather balloon being prepared for launch. It is filled with a fixed amount of helium gas on a warm day at sea level, but it is only partially inflated.

1. Why do you think scientists only partially inflate the balloon on the ground?
2. What variables change as the balloon rises into the atmosphere? (Think about the air outside the balloon and the gas inside).
3. Open the Ideal Gas Law Derivation (Scaffolded) simulation.

Part 2: Explore (Simulation Investigation)

In this simulation, you can select the dependent variable and explore how changing the other independent variables affects it.

Investigation A: The Relationship between Volume and Pressure (Boyle’s Law)

1. In the simulation, select Volume (V) as the dependent variable (this means it will change based on what you do to the others).
2. Keep the Temperature (T) and Amount (n) constant.
3. Move the Pressure (P) slider to increase and decrease the pressure.
4. Observe the macroscopic behavior of the container’s volume.
5. Observe the microscopic behavior of the particles (how fast they move, how often they hit the walls).
6. Record your data in the table below:

Investigation B: The Relationship between Volume and Temperature (Charles’s Law)

1. Keep Volume (V) as the dependent variable.
2. Set Pressure (P) to 1.00 atm and keep Amount (n) constant at 1.00 mol.
3. Move the Temperature (T) slider to increase and decrease the temperature. Temperature represents the average kinetic energy of the particles.
4. Observe the changes in Volume and particle motion.
5. Record your data:

Part 3: Explain (Sensemaking)

1. Based on your data in Investigation A, how does changing the macroscopic pressure affect the volume? Use the microscopic behavior of the particles (their motion and collisions with the container walls) to explain why this happens.
2. Based on your data in Investigation B, how does increasing the macroscopic temperature affect the volume? Explain this using the concept of kinetic energy of the particles. If the particles are moving faster (higher temperature), why must the volume increase to keep the pressure constant?
3. Combine these relationships: The Ideal Gas Law states that $PV = nRT$. Does this equation match your observations? Show mathematically how if $T$ and $n$ are constant, $P$ and $V$ must be inversely proportional.

Part 4: Elaborate/Evaluate (Argumentation & Modeling)

Now apply your findings back to our weather balloon phenomenon.

1. As the balloon rises, the outside atmospheric pressure decreases significantly. According to your simulation data, what will happen to the volume of the balloon due to this pressure change alone?
2. As the balloon rises, the temperature also drops significantly. According to your simulation data, what will happen to the volume of the balloon due to this temperature change alone?
3. In reality, both change at the same time. Use the simulation to model this: Set Volume (V) as the dependent variable. Lower the Pressure (to simulate high altitude) and lower the Temperature (to simulate cold air). What is the net effect on the Volume? Which factor (pressure drop or temperature drop) has a bigger influence on the final volume of the balloon?

Student Deliverable: Submit this completed handout with your data tables fully populated, and write a final 1-paragraph summary explaining how the kinetic energy and motion of particles lead to the macroscopic changes observed in the weather balloon.

Extension Options: If you finish early, research Avogadro’s Law. If you hold Pressure and Temperature constant but pump more gas particles into the balloon (increasing Amount $n$), what happens to the Volume? Verify your hypothesis using the simulation.

Peer Review: Trade your final paragraph with a partner. Review their explanation using the following criteria:

1. Did the author correctly describe the competing effects of both the dropping pressure and the dropping temperature on the balloon’s volume?
2. Did the author explicitly mention the kinetic energy (speed) of the particles?
3. Did the author connect the microscopic particle collisions to the macroscopic volume expansion?

Teacher Notes & Alignment:

• SEP: Developing and Using Models. Students use the simulation to model the relationships between macroscopic variables (P, V, T) and microscopic particle behavior.
• DCI: PS3.A: Definitions of Energy. Students connect macroscopic temperature to the microscopic kinetic energy (motion) of particles.
• CCC: Energy and Matter. Energy flows into or out of the system (changing temperature), affecting particle motion and the system’s macroscopic properties.
• Evidence Statements:
  • 1.a.ii: Students clearly depict both a macroscopic and a molecular/atomic-level representation of the system (using the simulation’s visuals and their written explanations).
  • 1.a.iii: Students depict forms of energy at two scales: macroscopic thermal energy (temperature) and molecular/atomic kinetic energy (motion of particles).
  • 2.a.ii: Thermal energy includes the kinetic energy of freely moving particles in gases. Students describe how changing temperature affects this kinetic energy and subsequently the volume/pressure.